2900 



Distribution of Prime Numbers 



2900 



Format's theorem (2 n + l prime), Cauchy's 



proof. Grunert, J. A. Grunert Arch. 30 



(1858) 357-. 

 Formula for primes. Mdrcker, . Crelle J. 



20 (1840) 350-. 

 . PervuUn, I. M. Kazan S. Ps.-Mth. 



Bll. 1 (1891) (Prot.) 70-; Fschr. Mth. 1 



(1892) 169. 

 (Pervusin). Lachtin, L. K. [1892] 



Eec. Mth. (Moscou) 16 (1893) 460- ; Fschr. 



Mth. (1892) 169-. 



( ). Cesdro,E. C. E.,119 (1894) 848-. 



Formulae for primes. Lucas, E. As. Fr. C. E. 



(1877) 159-. 

 . Gegenbauer, L. Wien Ak. Sb. 95 



(1887) (Ab. 2) 291-. 

 , approximate. PervuSin, I. Kazan 



S. Ps.-Mth. Bll. 4 (1895) (Prot.) 94-. 

 Function 6(n), development. Minin, A. P. 



Mosc. S. Sc. Bll. 93 (No. 2) (1898) 22; 



Fschr. Mth. (1898) 165. 

 Glaisher's factor tables and the distribution of 



primes. Johnson, W. W. A. Mth. 1 (1884- 



85) 15-. 

 Goldbach-Euler theorem. Sylvester, J. J. Nt. 



Haussner, B. D. Nf. 



Vh. (1896) (Th. 2, Halfte 1) 8-. 



. Stackel, P. Gott. Nr. (1896) 292-. 



and Bertrand's postulate. Catalan, E. C. 



Liege S. Sc. Mm. 15 (1888) No. 1, 30-, 108-. 



, function <f> (n) and its relation to. 

 Landau, E. Gott. Nr. (1900) 177-. 



, tables. Haussner, B. [1897] Ac. Nt. 



C. N. Acta 72 (1899) 1-. 

 , verification. Cantor, G. As. Fr. C. E. 



(1894) (Pt. 2) 117-. 

 Graphic determination of position. Wolf, B. 



Bern Mt. (1843) 28-. 

 primes. Kulik, J. P. Bohm. Gs. Ab. 



2 (1843) (Sect. B. 1842) 47-. 

 Infinity of primes. Gegenbauer, L. Wien Ak. 



Sb. 95 (1887) (Ab. 2) 94-. 

 contained in ax + b. Proof for a=8 



or 12. Serret, J. A. [1851] Liouv. J. Mth. 



17 (1852) 186-. 



, Euclid's theorem. Perott, J. Am. 

 J. Mth. 11 (1889) 99-; 13 (1891) 235-. 



Limits of prime of given form. Berton, V. I. 

 C. E. 74 (1872) 1390-. 



primes and a theorem of Legendre. 

 Desboves, A. H. N. A. Mth. 14 (1855) 281-. 



Mersenne's numbers. Lucas, E. Mess. Mth. 



7 (1878) 185-. 

 . Ball, W. W. B. Mess. Mth. 21 (1892) 



34-, 121. 

 . Cunningham, (Lt.-Col.) A. B. A. Ep. 



(1894) 563- ; (1895) 614 ; Nt. 51 (1894-95) 533. 

 Number and form of primes. Sludskii, T. A. 



[1866] (xn) Eec. Mth. (Moscou) 3 (1868) 



(Pt. 1) 214-. 



of prime and composite numbers between 

 given limits. PreobraSenskij , P. V . Eec. 

 Mth. (Moscou) 13 (1886) 707-; Fschr. Mth. 

 (1888) 170- . 



primes of form kp + l infinite if p is 

 prime. Kraus, L. Casopis 15 (1886) 61- ; 

 Fschr. Mth. (1886) 134-. 



below given limit. Kulik, J. P. 

 Bohm. Gs. Ab. 2 (1843) (Sect. B. 1841) 17-. 



. Biemann, B. Berl. Mb. 



(1859) 671-. 



Tortolini A. 3 (1860) 52-. 

 . Scheibner, W. Schlomilch 



. Hoffmann, K. E. Arch. 



Mth. Ps. 64 (1879) 333-. 

 . Jonquteres, E. de. C. E. 



95 (1882) 1144-, 1343- ; 96 (1883) 231-. 

 (de Jonquieres). Lipschitz, 



B. 0. S. C. E. 95 (1882) 1344-; 96 (1883) 



58-, 114-. 

 . Gram, J. P. [1884] Kjrfb. 



Dn. Vd. Selsk. Skr. 2 (1881-86) 183-. (With 



French resume".) 

 . Laar, J. J. van. N. Arch. 



Wisk. 16 (1889) 209- ; Fschr. Mth. (1889) 168. 

 . Bogel, F. Arch. Mth. Ps. 



7 (1889) 381-. 

 . Lorenz, L. Kjtfb. Dn. Vd. 



Selsk. Skr. 5 (1889-91) 427-; Fschr. Mth. 



(1891) 201-. 

 . Baranowski, A. [1894] 



Krk. Ak. (Mt.-Prz.) Ez. 8 (1895) 192- ; Crc. 



for 



Lebesgue, V. A. Liouv. J. Mth. 7 (1862) 



417-. 

 , proof. Kummer, E. E. Berl. Ak. 



Mb. (1878) '777-. 

 the series of primes. Perott, J. Bll. Sc. 



Mth. As. 5 (1881) (Pt. 1) 183- . 

 Integral connected with distribution of primes. 



Preobrazenskij, P. Kazan S. Nt. (Ps.-Mth.) 



P. 7 (1889) 5-; Fschr. Mth. (1889) 183-. 

 Large primes, determination. Euler, L. [1778] 



St Pet. Ac. Sc. N. Acta 13 (1802) 14-; 14 



(1805) 3-, 11-. 



, . Lucas, E. As. Fr. C. E. (1876) 61-. 



, . Cunningham, (Lt.-Col.) A., & 



Woodall, H. J. B. A. Ep. (1900) 646. 

 Law of distribution. Hargreave, C. J. Ph. 



Mg. 8 (1854) 114-. 

 Glaisher, J. W. L. B. A. Ep. 42 



(1872) (Sect.) 19-; Mess. Mth. 23 (1894) 97-. 



prime. Ac - Sc. Bll. (1894) 280-. 



Koch, H. von. C. E. 118 



(1894) 850-. 



(Eiemann's memoir, 1859). 



Mangoldt, H. von. [1894] Crelle J. Mth. 



114 (1895) 255-. 

 . Wigert, S. Stockh. Ofv. 



(1895) 341-. 



. Ajello, C. G. Mt. 34 



(1896) 14-. 



. Gram, J. P. Kj0b. Ov. 



(1897) 235-. 



. Bogel, F. Prag Sb. (1899) 



(Mth.-Nt.) No. 22, 20 pp. 

 . Kluyver, J. C. Amst. Ak. 



Vs. 8 (1900) 672-; Amst. Ak. P. 2 (1900) 



599-. 

 , function determining. 



Tchebicheff, P. [1848] St Pet. Mm. Sav. 



Etr. 6 (1851) 141-. 



226 



